How to output the first integer solution found in B&B process in Mosek

izng · July 1, 2024, 8:32am

Hi,

I want to know how to output the first integer solution and its objective value found within B&B process in Mosek.

mike_k · July 1, 2024, 2:02pm

Welcome!
This should work with a solver-specific callback (which is called each time an integer solution is found). According to the readme in the Mosek.jl this functionality is wrapped. Unfortunately, I did not find an example how to do that with JuMP.

blegat · July 4, 2024, 7:34am

Yes, apparently you can call putcallbackfunc(t::MSKtask, f::Function)

github.com

MOSEK/Mosek.jl/blob/91f62efd746fec35b391ae585bf1830aa169dcd5/src/msk_callback.jl#L92-L107


      
          """
              putcallbackfunc(t::MSKtask, f::Function)
          
          Set a callback. This will be called at various points during optimization. The `f` argument is a function of the form
          ```julia
              function(where::Callbackcode, dinf::Vector{Float64}, iinf::Vector{Int32}, liinf::Vector{Int64})
          ```
          There are very strict rules about what you can call from the callback
          function. Basically: Do not call anything using the same task as the
          callback was called from. The one exception is `getxx()` that can be called when solving a mixed integer problem.
          
          """
          function putcallbackfunc(t::MSKtask, f::Function)
              t.usercallbackfunc = f
              nothing
          end

The Mosek MOI wrapper in MosekTools.jl does not have any special support for it so you’ll have to use JuMP.unsafe_backend:

optimizer = unsafe_backend(model) # Gives you a `MosekTools.Optimizer`
task = unsafe_backend(model).task # Gives you a `Mosek.MSKtask`
function my_callback(where::Callbackcode, dinf::Vector{Float64}, iinf::Vector{Int32}, liinf::Vector{Int64})
    # ...
end
putcallbackfunc(task, my_callback)

By careful that the mapping between the JuMP variables and the indices in the Mosek task may be a bit nontrivial. JuMP.optimizer_index gives you the MOI.VariableIndex associated to the MosekTools.Optimizer. So given a JuMP variable x, do

index = JuMP.optimizer_index(x) # Gives a `MOI.VariableIndex` corresponding to the index in `optimizer`
col = MosekTools.mosek_index(optimizer, index) # Gives a `MosekTools.ColumnIndex`
col.value # Gives a `Int32` corresponding to the column in `task`

Let us know how it goes, we could add MOI attributes in MosekTools to make this easier